Blindly Factorizing 21 Quantumly

TL;DR

This paper presents a new classically verifiable scheme for blindly factorizing the semiprime 21 using quantum methods, improving on previous work that only handled 15, and introduces techniques for scaling blind quantum factorization.

Contribution

It introduces a novel scheme for blind quantum factorization of 21, incorporating non-Clifford gates and security checks applicable to larger semiprimes.

Findings

Successfully factorized 21 quantumly with a classical client

Extended security checks from 15 to 21

Proposed a photonic experiment setup for blind factorization

Abstract

We develop a classically verifiable scheme for blindly factorizing the semiprime 21 quantumly for a classical client who does not trust the remote quantum servers. Our scheme advances state of the art, which achieves blind factorization of 15 quantumly, by increasing the problem to factorizing the next semiprime, choosing a harder base, executing a non-Clifford gate, and showing that the security check for 15 also works for 21. Our algorithmic approach to incorporating non-Clifford operations sets the stage for scaling blind quantum factorization, whereas our five-EPR-pair scheme motivates a photonic experiment that supplants current demonstrations of blind factorization.